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Incubator Q&A Starting with 2014 "+" signs and 2015 "−" signs, you delete signs until one remains. What’s left?

Solution- Reasoning Two of the same sign collapse to +; two different signs collapse to -. This is isomorphic to the multiplication rules, so the entire question is isomorphic to: A large whit...

posted 2mo ago by Peter Taylor‭ · edited 2mo ago by Peter Taylor‭

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#2: Post edited by

Peter Taylor‭ · 2026-08-03T08:14:01Z (about 2 months ago)

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<details><summary>Solution</summary>-</details>
<details><summary>Reasoning</summary>
Two of the same sign collapse to +; two different signs collapse to -. This is isomorphic to the multiplication rules, so the entire question is isomorphic to:
~~> A large whiteboard has 2014 (+1) and 2015 (−1) written on it. You are allowed to replace two numbers by their product. Repeat until there is only one number left.</details>~~

<details><summary>Solution</summary>-</details>
<details><summary>Reasoning</summary>
Two of the same sign collapse to +; two different signs collapse to -. This is isomorphic to the multiplication rules, so the entire question is isomorphic to:
> A large whiteboard has 2014 (+1) and 2015 (−1) written on it. You are allowed to replace two numbers by their product. Repeat until there is only one number left.
Alternatively, and more formally: the replacement rules maintain the parity of the number of - signs. Since that number is initially odd, when only one sign remains it must be -.
</details>

#1: Initial revision by

Peter Taylor‭ · 2026-08-03T08:12:29Z (about 2 months ago)

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<details><summary>Solution</summary>-</details>

<details><summary>Reasoning</summary>
Two of the same sign collapse to +; two different signs collapse to -. This is isomorphic to the multiplication rules, so the entire question is isomorphic to:

> A large whiteboard has 2014 (+1) and 2015 (−1) written on it. You are allowed to replace two numbers by their product. Repeat until there is only one number left.</details>

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